Correct Answer: 15 km/hr

Solution : Let the speed of S as \(v\) km/hr.
Given that S gave a 500 m (or 0.5 km) head start to T, S has to run 5 km while T runs 4.5 km. Since they finish the race at the same time, their times are equal.
$⇒\frac{\text{Distance of S}}{\text{Speed of S}} = \frac{\text{Distance of T}}{\text{Speed of T}}$
Substituting the given values into the equation,
$⇒\frac{5}{v} = \frac{4.5}{13.5}$
$⇒v = \frac{5 \times 13.5}{4.5} = 15 $
Hence, the correct answer is 15 km/hr.

Correct Answer: 10

Solution : Given,
A sum becomes 4 times itself in 5 years
Time = 15 years
Let the principal be $P$.
So, interest in 5 years $\small=4P - P = 3P$
We know, Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$
⇒ Rate $= \frac{3P\times100}{P\times5}=60$%
In 15 years, the sum becomes:
$=P + \frac{\text{Principal × Rate × Time}}{100}$
$= P + \frac{P\times60\times15}{100}$
$=P + 9P$
$ = 10P$
Hence, the correct answer is 10.

Correct Answer: (7, 4, 33)

Solution : Given:
(8, 5, 39); (14, 11, 75)

Add the first and the second number and multiply the resultant number by 3 to obtain the third number in the given set of numbers.
⇒ (8, 5, 39)→(8 + 5) × 3 = 13 × 3 = 39
⇒ (14, 11, 75)→(14 + 11) × 3 = 25 × 3 = 75

Let's check the options –

First option: (12, 6, 70)→(12 + 6) × 3 = 18 × 3 = 54 ≠ 70
Second option: (9, 5, 54)→(9 + 5) × 3 = 14 × 3 = 42 ≠ 54
Third option: (11, 7, 74)→(11 + 7) × 3 = 18 × 3 = 54 ≠ 74
Fourth option: (7, 4, 33)→(7 + 4) × 3 = 11 × 3 = 33

So, only the fourth option follows the same pattern as followed by the given set of numbers. Hence, the fourth option is correct. 

Correct Answer: TENDER

Solution : Given:
ENDEARMENT

Now, let's compare all the option words with the word ENDEARMENT –
First option: TENT; The letter T appears only once in the word ENDEARMENT. But, in TENT, T appears two times. Therefore, all the letters of TENT are not present in the word ENDEARMENT.
Second option: TEMPER; P is not present in the word ENDEARMENT. Therefore, all the letters of TEMPER are not present in the word ENDEARMENT.
Third option: MEANS; S is not present in the word ENDEARMENT. Therefore, all the letters of MEANS are not present in the word ENDEARMENT.
Fourth option: TENDER; All the letters of TENDER are present in the word ENDEARMENT.

So, from the above, only TENDER can be formed from the word ENDEARMENT. Hence, the fourth option is correct.

Correct Answer: Gujarat

Solution : The correct answer is Gujarat.

Garba is a dance form that originated in Gujarat. The word garba refers to the social and religious event or gathering at which the dance is performed.

Correct Answer: Roger Binny

Solution : The correct answer is Roger Binny.

Former cricketer Roger Binny, who played a crucial role in India's 1983 World Cup victory, has assumed the role of President at the Board of Control for Cricket in India (BCCI). Taking over from former Indian cricket team captain Sourav Ganguly, Binny was appointed during the Annual General Meeting held at Mumbai's Taj Hotel.

Correct Answer: 216 cubic metres

Solution : Given:
Side length = 6 m
Volume of the cube = (side)³ = 6³ = 216 cubic metres
Hence, the correct answer is 216 cubic metres.

Correct Answer: 8 : 5

Solution : 50% of A is equal to 80% of B
⇒ $\frac{50}{100}\times{\text{A}} = \frac{80}{100}\times{\text{B}}$
⇒ 5A = 8B
⇒ A : B = 8 : 5
Hence, the correct answer is 8 : 5.

Correct Answer: 194 : 12

Solution : Let's check the options –
First option: 187 : 11; 187 ÷ 11 = 17; 187 is divisible by 11.
Second option: 194 : 12; 194 ÷ 12 = 16.17; 194 is not divisible by 12.
Third option: 195 : 13; 195 ÷ 13 = 15; 195 is divisible by 13.
Fourth option: 224 : 14; 224 ÷ 14 = 16; 224 is divisible by 14.

So, the second option is different from the other three options as 194 is not divisible by 12. Hence, the second option is correct.

Correct Answer: 54

Solution : Here, diagonally opposite numbers are thrice of the number (7, 14, and 18).
Like, 21 = 7 × 3
And, 42 = 14 × 3
Similarly, 18 × 3 = 54

So, the missing number in the figure is 54. Hence, the fourth option is correct.